Rotational Organization Theory of Gravitational Concentration (ROTGC): A Fiber Bundle and Persistent Homology Approach to Hierarchical Structure Formation

Rotational Organization Theory of Gravitational Concentration (ROTGC) Version 2.0 presents a unified physical and mathematical framework for investigating the long-term organizational processes that lead to the formation of gravitationally concentrated astrophysical structures. The theory does not replace or modify Newtonian gravity or General Relativity. Instead, it examines how differential rotation, shear, torque generation, angular-momentum transport, radial matter-energy transport, and conservation laws collectively influence the evolution of central concentration. The framework is developed from established principles of mass-energy, linear momentum, and angular-momentum conservation. Advanced mathematical tools—including differential geometry, fiber bundles, persistent homology, and sheaf-theoretic multiscale representations—are introduced only after the physical formulation has been established and serve as coordinate-independent mathematical descriptions rather than new physical postulates. ROTGC introduces measurable organizational quantities describing central concentration, rotational organization, and angular-momentum transport, together with explicit observational tests based on galaxy rotation curves, weak gravitational lensing, accretion systems, compact objects, black holes, Event Horizon Telescope observations, gravitational-wave catalogs, and large-scale structure surveys. The theory makes falsifiable predictions and explicitly specifies failure criteria. It introduces no new fundamental force, matter component, or physical field, and remains fully consistent with established conservation laws and General Relativity within their accepted domains.